The reaction `SO_(2)Cl_(2) overset(k_(1))rarr SO_(2)+Cl_(2)` is a first order reaction with `k_(1) = 2.2 xx 10^(-5) s^(-1)` at `575 K`. What percentage of `SO_(2)Cl_(2)` will get decomposed in `90 min` when the reaction is carried out at `575 K`.

Explanation

Since the reaction is of the first order (given)
`k = (2.303)/(t)log.(a)/(a-x)` and `k = 2.2 xx 10^(-5) s^(-1)`
`t = 90 min = 90 xx 60 = 5400 s` (given)
`:. 2.2 xx 10^(-5) = (2.303)/(5400) log.(a)/(a-x)`
or `log.(a)/(a-x) = 0.0516`
or `(a)/(a-x)= "antilog"(0.0516) = 1.127`
or `a = (a-x) 1.127` or `a = a(1.127) - x(1.127)`
or `0.127a = 1.127 x`
`:. (x)/(a) = (0.127)/(1.127) = 0.113 = 11.3%`